Find the LCM and HCF of 8, 9 and 25 Using Prime Factorization

Video Explanation

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Solution

Question: Find the LCM and HCF of the integers 8, 9 and 25 by applying the prime factorization method.

Step 1: Prime Factorization of the Given Integers

8 = 2 × 2 × 2 = 2³

9 = 3 × 3 = 3²

25 = 5 × 5 = 5²

Step 2: Find the HCF

There is no common prime factor among 8, 9 and 25.

∴ HCF (8, 9, 25) = 1

Step 3: Find the LCM

LCM is the product of the highest powers of all prime factors:

LCM = 2³ × 3² × 5²

LCM = 1800

Final Answer

HCF of 8, 9 and 25 = 1
LCM of 8, 9 and 25 = 1800

Conclusion

Thus, by using the prime factorization method, we find that the HCF of 8, 9 and 25 is 1 and their LCM is 1800.